Assume that the total revenue received from the sale of x items is given by, R(x)equals34 ln (4 x plus 5 ), while the total c
1 answer:
Answer:
63 units
Step-by-step explanation:
The profit function P(x) is given by the revenue function minus the cost function:
The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:
The number of units that should be manufactured so that profit is maximum is 63 units.
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Answer:
Step-by-step explanation:
P = x^2 + 6
Solving for 4x^2:
P = x^2 +6
P - 6 = x^2
4(P - 6) = 4x^2
Substitution:
Answer:
The inverse of a non-function mapping is not necessarily a function.
For example, the inverse of the non-function mapping is the same as itself (and thus isn't a function, either.)
Step-by-step explanation:
A mapping is a set of pairs of the form . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.
A mapping is a function if and only if for each possible input value , at most one of the distinct pairs includes
as the value of first entry.
For example, the mapping is a function. However, the mapping
isn't a function since more than one of the distinct pairs in this mapping include
as the value of the first entry.
The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping is the mapping
.
Consider mapping . This mapping isn't a function since the input value
is the first entry of more than one of the pairs.
Invert as follows:
becomes
becomes
.
becomes
In other words, the inverse of the mapping would be
, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)
Thus, is an example of a non-function mapping that is still not a function.
More generally, the inverse of non-trivial ellipses (a class of continuous non-function mappings, including circles) are also non-function mappings.